Move the stack from peg A to peg C, never putting a bigger disk on a smaller one. The catch: the optimal solution is 2ⁿ − 1 moves, so 8 disks means 255 moves — recursion made visible. Solve it yourself, or watch the algorithm do it.
To move n disks from A to C: move the top n−1 disks from A to B (using C), move the biggest disk A→C, then move the n−1 disks B→C. That self-reference is exactly what recursion is. The move count doubles each disk, which is why legend says the world ends at 64 disks: 2⁶⁴−1 ≈ 1.8×10¹⁹ moves.